Statistical evaluation of methods for the calculation of static formation temperatures in geothermal and oil wells using an extension of the error propagation theory

The feasibility of using the more sophisticated weighted least-squares (WLS) model, as opposed to the traditional ordinary least-squares (OLS), in linear regressions of BHT data to estimate the static formation temperatures (SFT) was investigated. The most commonly used analytical methods (line-source; spherical and radial heat flow; and cylindrical heat source) were applied. Error propagation equations were derived to calculate errors in the time function of each method. These errors were combined with the BHT measurement errors to compute weighting factors for applying the WLS. Intercept uncertainties were estimated for all regressions using sets of synthetic and actual borehole logs taken from geothermal and oil applications. SFT computed with the spherical and radial heat flow method were generally greater than those from the other two methods.     

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Water temperature behaviour in the River Loire since 1976 and 1881

Analysis of monthly mean river temperatures, recorded on an hourly basis in the middle reaches of the Loire since 1976, allows reconstruction by multiple linear regression of the annual, spring and summer water temperatures from equivalent information on air temperatures and river discharge. Since 1881, the average annual and summer temperatures of the Loire have risen by approximately 0.8?°C, this increase accelerating since the late 1980s due to the rise in air temperature and also to lower discharge rates. In addition, the thermal regime in the Orleans to Blois reach is considerably affected by the inflow of groundwater from the Calcaires de Beauce aquifer, as shown by the summer energy balance. To cite this article: F. Moatar, J. Gailhard, C. R. Geoscience 338 (2006).     

近几十年我国极端气温变化特征分区方法探讨

采用聚类统计检验分析和旋转主分量分析相结合确定中心站的方法,利用我国多年极端气温资料,对我国最高和最低气温年际变化型态进行区划。结果表明,这两种方法结合可以互相补充,使分区结果更具客观性。中国极端高温和极端低温年际变化分别可划为12和11个不同类型的区域,分别计算了各区域第一主成分的方差贡献率以及各区域之间的两两相关系数,检验证明分区是合理的。     

The distribution of radiogenic heat production as a function of depth in the Sierra Nevada Batholith, California

Geochemical analyses and geobarometric determinations have been combined to create a depth vs. radiogenic heat production database for the Sierra Nevada batholith, California. This database shows that mean heat production values first increase, then decrease, with increasing depth. Heat production is 2 μW/m³ within the 3-km-thick volcanic pile at the top of the batholith, below which it increases to an average value of 3.5 μW/m³ at 5.5 km depth, then decreases to 0.5–1 μW/m³ at 15 km depth and remains at these values through the entire crust below 15 km. Below the crust, from depths of 40–125 km, the batholith's root and mantle wedge that coevolved beneath the batholith appears to have an average radiogenic heat production rate of 0.14 μW/m³. This is higher than the rates from most published xenolith studies, but reasonable given the presence of crustal components in the arc root assemblages. The pattern of radiogenic heat production interpreted from the depth vs. heat production database is not consistent with the downward-decreasing exponential distribution predicted from modeling of surface heat flow data. The interpreted distribution predicts a reasonable range of geothermal gradients and shows that essentially all of the present day surface heat flow from the Sierra Nevada could be generated within the 35 km thick crust. This requires a very low heat flux from the mantle, which is consistent with a model of cessation of Sierran magmatism during Laramide flat-slab subduction, followed by conductive cooling of the upper mantle for 70 m.y. The heat production variation with depth is principally due to large variations in uranium and thorium concentration; potassium is less variable in concentration within the Sierran crust, and produces relatively little of the heat in high heat production rocks. Because silica content is relatively constant through the upper 30 km of the Sierran batholith, while U, Th, and K concentrations are highly variable, radiogenic heat production does not vary directly with silica content.     

Surface temperature differences between minerals in crystalline rocks: Implications for granular disaggregation of granites through thermal fatigue

Thermal expansion differences between minerals within rocks under insolation have previously been assumed to drive breakdown by means of granular disaggregation. However, there have been no definitive demonstrations of the efficacy of this weathering mechanism. Different surface temperatures between minerals should magnify thermal expansion differences, and thus subject adjacent minerals to repeated stresses that might cause breakdown through fatigue failure. This work confirms the existence of surface temperature differences between minerals in granitic rocks under simulated short-term temperature fluctuations so as to discriminate their potential for initiating granular disaggregation. The influence of colour, as a surrogate for albedo, and crystal size, as a function of thermal mass are specifically identified because of their ease of quantification. Four rock types with a range of these properties were examined, and subjected to repeated short-term temperature cycles by radiative heating and cooling under laboratory conditions. Results show that while albedo is the main control for overall and individual maximum temperatures, crystal size is the main factor controlling higher temperature differences between minerals. Thus, stones with large differences of mineral sizes can undergo magnified stresses due to thermal expansion differences.     

Climatic characteristics of summer high temperature and assessment methods in the large cities of North China

Based on the high temperature data of June to August in 1961-2000 in North China, the high temperature weather processes are investigated, and a more complete data set for severe high temperature processes is created. The climatic characteristics of adverse high temperature weather in Beijing, Tianjin, Shijiazhuang, Jinan and Taiyuan are analyzed respectively. The major features of the East-Asia Subtropical High and Transformed Continental High are discussed. The outcomes indicate that the influence of both East Asia Subtropical High and Transformed Continental High on these weather events varies, by a larger margin, from one city to another over North China and they are also closely related to the relative humidity. It is found that the behaviours of East-Asia Subtropical High and Transformed Continental High are the major important systems that give rise to the summer high temperature weather over the region. Based on these findings, the 5-day, 10-day and monthly assessment models for such high impact events have been developed. The assessment outcomes prove to be useful in assessing severe high-temperature events in major cities of North China.     

Climate change in Mt. Qomolangma region since 1971

Using monthly average, maximum, minimum air temperature and monthly precipitation data from 5 weather stations in Mt. Qomolangma region in China from 1971 to 2004, climatic linear trend, moving average, low-pass filter and accumulated variance analysis methods, the spatial and temporal patterns of the climatic change in this region were analyzed. The main findings can be summarized as follows: (1) There is obvious ascending tendency for the interannual change of air temperature in Mt. Qomolangma region and the ascending tendency of Tingri, the highest station, is the most significant. The rate of increasing air temperature is 0.234 oC/decade in Mt. Qomolangma region, 0.302 oC/decade in Tingri. The air temperature increases more strongly in non-growing season. (2) Compared with China and the global average, the warming of Mt. Qomolangma region occurred early. The linear rates of temperature increase in Mt. Qomolangma region exceed those for China and the global average in the same period. This is attributed to the sensitivity of mountainous regions to climate change. (3) The southern and northern parts of Mt. Qomolangma region are quite different in precipitation changes. Stations in the northern part show increasing trends but are not statistically significant. Nyalam in the southern part shows a decreasing trend and the sudden decreasing of precipitation occurred in the early 1990s. (4) Compared with the previous studies, we find that the warming of Mt. Qomolangma high-elevation region is most significant in China in the same period. The highest automatic meteorological comprehensive observation station in the world set up at the base camp of Mt. Qomolangma with a height of 5032 m a.s.l will play an important role in monitoring the global climate change.     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.